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Reasoning Determine Whether The Lines Will Be Essay

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¶ … Reasoning

Determine whether the lines will be perpendicular when graphed.

2x + 3y = 6

The slope of perpendicular lines are the negative reciprocal of one another, therefore will solve for the slope of each line. Slope can be determined by solving for m in the equation y= mx +b where m is the slope.

3x-2y=

3x-2y-3x= 6-3x

-2y= -3x +

y = 3x/2 -- 3

m= 3/2

2x + 3y = 6

2x = 6- 2x

3y= 6-2x

y = 2 -- 2x/3

m= -2/3

Because the slopes are negative reciprocals, the lines are perpendicular.

Alice's Restaurant has a total of 205 seats. The number of seats in the non-smoking section is 73 more than twice the number of seats in the smoking section. How many seats are in each section?

N= 73 + 2S

N+S = 205

+ 2S + S = 205

+ 3S =205

3S= 205-73

3S=132

S=

N= 73 + 2S

N= 73 + 2*

N= 73 +

N= 161

There are 44 seats in the smoking section and 161 seats in the non-smoking section.

Solve the system of equations by the substitution method

x + 3y = 32

-3x + 2y = 3

x + 3y = 32

x= 32-3y

-3x + 2y = 3

-3(32-3y) + 2y = 3

-96 + 9y + 2y = 3

-96 + 11y=3

11y= 96 + 3

11y= 99

y= 9

x = 32-3y

x= 32-(3*9)

x= 32-27

x=5

4. Solve the system of equations x + y = 5

x - y = -9

x + y = 5

x - y = -9

x= -9 + y x + y = 5

-9 + y + y = 5

-9 + 2y = 5

2y = 14

y=7

x-7 = -9

x= -9 + 7

x= -2

5. Ricks Paint Store sells a special shade of pink paint (Ricky's Blush) which can be made from red paint and white paint. The amount of red paint should be three times the amount of white paint. How much of each kind of paint is needed to make 264 gallons of Ricky's Blush?

R=3W

R + W = 264

3W + W = 264

4W = 264

W= 66 gallons of white

R= 3 * 66

R = 198 gallons of red

One needs 66 gallons of white paint and 198 gallons of red paint in order to make Ricky's Blush.

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